High frequency (HF) radio channels, very-high frequency (VHF) radio channels, and ultra-high frequency (UHF) radio channels all exhibit time and frequency dispersion (i.e., delay spread and Doppler spread) due to the presence of signal reflectors or scatterers in the environment, as well as the relative motion of transmitters and receivers. As a result, the channel experiences distortion which can cause transmitted symbols to be incorrectly interpreted at the receiving device. Doppler spreading can cause the delay spread (i.e. multipath) to vary with time. These phenomena typically require modems to employ equalization to track and compensate for the time-varying multipath channel.
For coherent demodulation of multi-carrier waveforms, such as orthogonal frequency division multiplexing (OFDM) waveforms, for example, pilot tones are inserted in the waveform. In the case of OFDM waveforms, the pilot tones are interspersed with the data being transmitted, and guard bands are positioned on either side of the data to separate one frame of data from the next. How many and how often to insert pilot tones in a waveform is usually decided based upon expected worst case multipath and fading conditions. Data in between pilot tones is interpolated to generate channel estimates for the data tones to allow demodulation. Such interpolation is usually based on expected worst case scenarios.
By way of example, U.S. Pat. No. 6,654,429 to Li discloses a method and apparatus for pilot-symbol aided channel estimation in a wireless digital communication system which transmits packets of N OFDM data blocks, where each data block includes a set of K orthogonal carrier frequencies. At the transmitter, pilot symbols are inserted into each data packet at known positions to occupy predetermined positions in the time-frequency space. At the receiver, the received signal is subject to a two-dimensional inverse Fourier transform, two-dimensional filtering and a two-dimensional Fourier transform to recover the pilot symbols so as to estimate the channel response.
In an article entitled “Time versus Frequency Domain Channel Estimation for OFDM Systems with Antenna Arrays,” Cheng et al. compare channel estimation schemes in the time and frequency domains in terms of error performance of both the estimated channel impulse response (CIR) and transfer function (TF) as well as the resulting bit-error rate (BER) in an orthogonal frequency-division multiplexing (OFDM) system with a time-multiplexed preamble. Cheng et al. determined that if a total number of sub-carriers K exceeded a number of taps L in the CIR, the TF estimate based on the time domain least squares (LS) scheme was more accurate than the one obtained from direct LS estimation in the frequency domain.
Despite such approaches, improved techniques for performing channel estimate interpolation for demodulating multi-carrier waveforms are still desirable in many applications.